On Slater's condition and finite convergence of the Douglas-Rachford algorithm
Abstract
The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility problems. Our analysis builds upon, and considerably extends, pioneering work by Spingarn. Specifically, we obtain finite convergence in the presence of Slater's condition in the affine-polyhedral and in a hyperplanar-epigraphical case. Various examples illustrate our results. Numerical experiments demonstrate the competitiveness of the Douglas-Rachford algorithm for solving linear equations with a positivity constraint when compared to the method of alternating projections and the method of reflection-projection.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2015
- DOI:
- 10.48550/arXiv.1504.06969
- arXiv:
- arXiv:1504.06969
- Bibcode:
- 2015arXiv150406969B
- Keywords:
-
- Mathematics - Optimization and Control;
- Primary 47H09;
- 90C25;
- Secondary 47H05;
- 49M27;
- 65F10;
- 65K05;
- 65K10
- E-Print:
- Journal of Global Optimization, 65(2):329--349, 2016